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A new photometry and period analysis of the Algol-type binary XZ And
New Astronomy 25 (2013) 109–113
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A new photometry and period analysis of the Algol-type binary XZ And Y.-G. Yang ⇑ School of Physics and Electronic Information, Huaibei Normal University, 235000 Huaibei City, Anhui Province, China
h i g h l i g h t s We model new BVR light curves. We detected a periodicity in the O—C curve and provided two possible mechanisms. The secular period increase may result from mass transfer. We proposed the possible evolutionary statue.
a r t i c l e
i n f o
Article history: Received 25 March 2013 Received in revised form 30 April 2013 Accepted 6 May 2013 Available online 17 May 2013 Communicated by E.P.J. van den Heuvel Keywords: Stars: binary: close Binaries: eclipsing Stars: individual (XZ And)
a b s t r a c t We present multi-color photometry of the eclipsing binary XZ And, obtained on 2010 October and November with the 60-cm telescope at Xinglong station of National Astronomical Observatories of China. Using the updated W–D program, the photometric elements were deduced from BVR light curves. The results imply that XZ And is a classic Algol-type binary, whose secondary component fills its Roche lobe. The mass ratio and fill-out factor of the primary are q ¼ 0:474ð0:003Þ and f1 ¼ 68:3ð0:6Þ%, respectively. Based on photometric and CCD light minimum times, we constructed the O—C curve, which may be described by an upward parabolic line with a quasi-cyclic variation, i.e., light-time orbit. The period and semi-amplitude are Pmod ¼ 32:30ð0:06Þ yr and A ¼ 0:d 0368ð0:d 0008Þ, respectively. This kind of cyclic variation may result from either magnetic activity of the secondary star or light-time effect due to the unseen third body. The long-term period increases at a rate of dP=dt ¼ þ5:37ð0:41Þ 107 d yr1 , which may be interpreted by the conservative mass transfer from the secondary component to the primary one. With period increasing, the binary may become wider. Finally, XZ And (i.e., 2:15M þ 1:02M ) will transformed into a binary system consisting of a WD and an unevolved companion. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The light variability of XZ And (=BD + 41°367, aJ2000:0 ¼ 01h 56m 51:s 53 and dJ2000:0 ¼ þ42 060 02.00 15) was discovered by Miss Leavitt (Shapley, 1923). Hill et al. (1975) preliminarily determined a spectral type of A4IV-V, while Halbedel (1984) reclassified it as A1V. The variable’s magnitude ranges from 10:m 8 to 11:m 9 and the color index is B V ¼ 0:8 (Malkov et al., 2006). Visual observations were published by Leiner (1926); Kordylewska (1931); Lause (1934) and Lause (1936), respectively. Blitzstein (1954) and Reinhardt (1967) obtained two sets of photoelectric light curves, which were analyzed by Giuricin et al. (1980) who derived a mass ratio of 0.4. Dugan and Wright (1939) determined a period of 1:d 357283 and found some irregular variations in the ðO—CÞ curve. Demircan et al. (1995) summarized 16 linear ephemerides
⇑ Tel.: +86 561 3803256; fax: +86 561 3804931. E-mail address: [email protected] 1384-1076/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.newast.2013.05.001
for XZ And, implying that changes may exist in its orbital period. Based on different databases of eclipse times, several authors subsequently attempted to model the distorted ðO—CÞ curve in two ways (i.e., sine curves, and an upward parabola with a cyclic sine-shape modulation). The cyclic modulation possibly includes one period (Frieboes-Conde and Herczeg, 1973), two periods (Odinskaya and Ustinov, 1952; Todoran, 1967; Borkovits and Hegedüs, 1996; Selam and Demircan, 1999), and three ones (Demircan et al., 1995). The ðO—CÞ curve of XZ And was alternatively characterized by a secular period variation superimposed with a cyclic oscillation (Kreiner, 1971; Kreiner, 1976; Rafert, 1982). Due to those inconsistent results for XZ And, it is necessary to reanalyze the orbital period changes. In this paper, new photometry of XZ And is presented. The primary aim is to study period variation and evolutionary state. Multi-color observations and data reduction are described in Section 2. The period changes are reanalyzed in Section 3 and photometric models considered in Section 4. Finally, some results of XZ And are briefly discussed in Section 5.
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2. New observations Complete light curves of XZ And were obtained on eight nights of 2010 October and November, using the 60-cm telescope at the Xinglong station (XLs) of National Astronomical Observatories of China (NAOC). This telescope was equipped with a PI 1024 1024 CCD photometric system. The plate-scale is 0.00 99 per pixel, and the resulting size of the effective field of view is 170 170 . The standard Johnson–Cousin–Bessel set of BVRI filters was used. Data reduction was performed by using the Image Reductions and Analysis Facility (IRAF) software in the standard fashion. In the observing process, we chose BDþ41 379 and TYC 28241778-1 as the comparison and check stars. Typical exposure times for BVR bands are 45 s;35 s, 25 s, respectively. A total of 2975 effective images (i.e., 994 in B band, 989 in V band and 992 in R band) was obtained. The individual observations (i.e., HJD and Dm) are available on request. The mean errors in the differences between the magnitude of the check star and that of the comparison one were estimated to be 0:006 mag, 0:005 mag and 0:005 mag for BVR bands, respectively. The observed light curves are plotted in the left panel of Fig. 1, where phases were computed by a period of 1:d 35727963 (Kreiner et al., 2001). From this figure, XZ And is a typical EA-type eclipsing binary (Binnendijk, 1975). The variable light amplitudes are 2:m 90, 2:m 45 and 2:m 07 in BVR bands, which approximately agree with the estimated value of 2:m 97 in B band from Malkov et al. (2006). Using the 85-cm telescope (Zhou et al., 2009), another photometry of primary eclipse of XZ And was obtained on 2012 October 25, which is shown in the right panel of Fig. 1. From those observations, we determined several light minimum times, which are listed in Table 1.
Table 1 New light minimum timings of XZ And. JD (Hel.)
Min
Error
Band
2455474.35865 2455474.35847 2455474.35870 2455479.10554 2455479.10802 2455479.10332 2455481.14476 2455481.14474 2455481.14493 2455521.19063 2455521.18311 2455521.18505 2456226.29034 2456226.29029 2456226.29032
I I I II II II I I I II II II I I I
±0.00012 ±0.00014 ±0.00013 ±0.00065 ±0.00048 ±0.00074 ±0.00007 ±0.00010 ±0.00012 ±0.00149 ±0.00099 ±0.00010 ±0.00007 ±0.00008 ±0.00010
B V R B V R B V R B V R B V R
Min:I ¼ HJD2424152:2546 þ 1:d 35727963 E;
ð1Þ
we can calculate the residuals ðO—CÞ, which are listed in Table 2 and displayed in the upper panel of Fig. 2. From this figure, the general trend of the ðO—CÞ curve may be described by an upwards parabolic superimposed with a quasi-cyclic variation, i.e., a light-time orbit (Irwin, 1952). Using the nonlinear least-squares method (Press et al., 1992), we obtained the following equation,
O—C ¼ 0:0540ð0:0020Þ þ 1:35726055ð0:00000025Þ E þ 9:87ð0:08Þ 1010 E2 þ s
ð2Þ
and
1 e2 sinðm þ xÞ þ e sin x ; 1 þ e cos m
3. Reanalyzing period variations
s¼A
The complicated period variations of XZ And were studied by many authors, who gave some inconsistent results. Due to large measurement errors for visual and photographic observations, the ðO—CÞ curve could not be described well, which can be seen directly from the literature such as Borkovits and Hegedüs (1996) and Selam and Demircan (1999). Therefore, we collected all available high-precision observations, including 18 photoelectric and 48 CCD measurements. Table 2 listed those eclipsing times spanning over 64 years from 1948 to 2012. Using the linear ephemeris (Kreiner et al., 2001),
where A ¼ a12 =c is the semi-amplitude of the light-time orbit, and several other parameters are taken from Irwin (1952). The fitted parameters are listed as follows, A ¼ 0:d 0368ð0:d 0008Þ, Pmod ¼ 32:30ð0:06Þ yr; e ¼ 0:191ð0:009Þ, x ¼ 3:923ð0:047Þ and T p ¼ HJD2446108:9ð118:0Þ. The final residuals are listed in Table 2, and are shown in the lower panel of Fig. 2, where no regularity is apparent. In its upper panel, the solid and dotted lines are Eq. (2) and its parabolic part, respectively. The quadratic term represents a continuous increase of the orbital period at a rate of dP=dt ¼ þ5:37ð0:41Þ 107 d yrs1 . The modulation period is
ð3Þ
Fig. 1. Left panel: BVR light curves of XZ And, observed in 2010 using the 60-cm telescope. Right panel: the primary eclipse, obtained on 2012 October 25 using the 85-cm telescope.
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Y.-G. Yang / New Astronomy 25 (2013) 109–113 Table 2 All compiled photoelectric and CCD eclipsing times for XZ And. JD (Hel.)
Epoch
Method
Min.
O—C
Residuals
Ref
2432883.605 2432887.676 2432955.540 2433180.847 2433206.635 2433231.7415 2439020.5507 2439033.4452 2440484.3930 2442742.2476 2443779.8763 2443809.7364 2443847.7403 2444257.6387 2444542.6659 2449313.5336 2449651.4992 2449655.5713 2450008.4732 2450430.6000 2450443.5030 2451486.6001 2451512.3884 2451881.5782 2452279.2714 2452321.3483 2452530.3718 2452534.4460 2452542.5899 2452934.8526 2452940.2820 2452949.7827 2452975.5716 2453267.3919 2453318.9701 2453335.2573 2453348.8308 2453644.7240 2453681.3712 2453715.3055 2453952.8326 2454012.5539 2454381.7406 2454429.2461 2454468.6076 2454469.2861 2454476.7520 2454708.8488 2454779.4277 2454799.7876 2454824.2181 2454863.5797 2455084.8180 2455140.4666 2455187.2939 2455239.5488 2455423.4600 2455474.3586 2455479.1056 2455481.1448 2455521.1863 2455561.2242 2455563.9386 2455842.1809 2456226.2913 2456265.6514
+6433.0 +6436.0 +6486.0 +6652.0 +6671.0 +6689.5 +10954.5 +10964.0 +12033.0 +13696.5 +14461.0 +14483.0 +14511.0 +14813.0 +15023.0 +18538.0 +18787.0 +18790.0 +19050.0 +19361.0 +19370.5 +20139.0 +20158.0 +20430.0 +20723.0 +20754.0 +20908.0 +20911.0 +20917.0 +21206.0 +21210.0 +21217.0 +21236.0 +21451.0 +21489.0 +21501.0 +21511.0 +21729.0 +21756.0 +21781.0 +21956.0 +22000.0 +22272.0 +22307.0 +22336.0 +22336.5 +22342.0 +22513.0 +22565.0 +22580.0 +22598.0 +22627.0 +22790.0 +22831.0 +22865.5 +22904.0 +23039.5 +23077.0 +23080.5 +23082.0 +23111.5 +23141.0 +23143.0 +23348.0 +23631.0 +23660.0
pe pe pe pe pe pe pe pe pe pe pe pe pe pe pe CCD pe pe pe CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD
I I I I I II II I I II I I I I I I I I I I II I I I I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I II I II I II I II I I I I I
0.0295 0.0303 0.0303 0.0317 0.0320 0.0352 0.0236 0.0233 0.0074 +0.0125 +0.0010 +0.0009 +0.0010 +0.0009 0.0006 +0.0292 +0.0322 +0.0325 +0.0416 +0.0545 +0.0633 +0.0910 +0.0910 +0.1008 +0.1110 +0.1123 +0.1147 +0.1171 +0.1173 +0.1262 +0.1264 +0.1262 +0.1268 +0.1320 +0.1335 +0.1334 +0.1341 +0.1403 +0.1410 +0.1433 +0.1464 +0.1474 +0.1541 +0.1548 +0.1552 +0.1550 +0.1559 +0.1579 +0.1582 +0.1590 +0.1584 +0.1589 +0.1606 +0.1608 +0.1619 +0.1616 +0.1614 +0.1620 +0.1585 +0.1618 +0.1635 +0.1617 +0.1615 +0.1615 +0.1618 +0.1608
0.0046 0.0053 0.0035 +0.0012 +0.0015 0.0010 +0.0054 +0.0055 0.0019 +0.0027 0.0036 0.0034 0.0029 +0.0014 +0.0035 +0.0072 +0.0001 +0.0003 0.0015 0.0017 +0.0067 +0.0027 +0.0019 +0.0012 +0.0006 +0.0008 0.0021 +0.0002 +0.0002 0.0003 0.0002 0.0006 0.0006 0.0017 0.0013 0.0017 0.0013 0.0008 0.0008 +0.0009 +0.0000 +0.0000 +0.0014 +0.0015 +0.0014 +0.0012 +0.0020 +0.0014 +0.0010 +0.0016 +0.0008 +0.0009 +0.0007 +0.0005 +0.0013 +0.0007 0.0006 0.0002 0.0037 0.0004 +0.0011 0.0009 0.0011 0.0019 0.0019 0.0029
(1) (1) (1) (1) (1) (2) (2) (3) (4) (5) (6) (6) (6) (6) (6) (7) (8) (8) (9) (10) (11) (12) (13) (14) (15) (16) (16) (17) (14) (18) (19) (20) (14) (21) (18) (22) (18) (23) (22) (22) (23) (24) (25) (26) (25) (27) (25) (28) (29) (30) (29) (30) (31) (32) (32) (31) (33) (34) (34) (34) (34) (35) (36) (36) (34) (37)
Refs. (1) Blitzstein (1954); (2) Kreiner (1976); (3) Frieboes-Conde and Herczeg (1973); (4) Pohl and Kizilirmak (1970); (5) Brancewicz and Kreiner (1976); (6) Olson (1981); (7) Hawkins and Downey (1994); (8) Hegedüs et al. (1996); (9) Müyesseroglu et al. (1996); (10) Baldwin and Samolyk 1997; (11) Paschke (1999); (12) Baldwin and Samolyk (2000); (13) Agerer and Hübscher (2001); (14) Baldwin and Samolyk (2004); (15) Diethelm (2002); (16) Agerer and Hübscher (2003); (17) Borkovits et al. (2003); (18) Cook et al. (2005); (19) Hübscher (2005); (20) Nelson (2004); (21) Hübscher et al. (2005); (22) Hübscher et al. (2006); (23) Baldwin and Samolyk (2007); (24) Biró et al. (2007); (25) Samolyk (2008a); (26) Hübscher et al. (2008); (27) Brát et al. (2008); (28) Samolyk (2008b); (29) Hübscher et al. (2009); (30)Samolyk (2009); (31) Samolyk (2010); (32) Erkan et al. (2010); (33) Dogru et al. (2011); (34) Present work; (35) Brát et al. (2011); (36) Nagai (2012); (37) Diethelm (2013).
Fig. 2. The O—C curve of the eclipsing binary XZ And. The filled circles represent photoelectric or CCD observations. The solid and dotted lines are constructed by all the contribution of Eq. (2) and only its parabolic part, respectively.
a bit smaller than the value of 35:6 yr from Borkovits and Hegedüs (1996). 4. Photometric solution Multi-bandpass observations of XZ And were simultaneously analyzed using the 2003-version W–D program (Wilson and Devinney, 1971; Wilson, 1990), which is widely used for modeling the photometric light curves of eclipsing binaries as a standard tool. The bolometric albedos and gravity darkening coefficients were adopted as A1 ¼ 1 and g 1 ¼ 1 for the primary with radiative envelope, A2 ¼ 0:5 and g 2 ¼ 0:32 for the secondary with radiative one (Lucy, 1967; Rucinski, 1969; and von Zeipel, 1924). Meanwhile, the logarithmic bolometric (X and Y) and monochromatic (x and y) limb-darkening coefficients were taken from the tables of van Hamme (1993). During the calculation, the five adjustable parameters i, q; T 2 ; X1 , and L1 were used. According to the spectral type A1 of XZ And (Halbedel, 1984), the mean effective temperature of the primary component was fixed to be T 1 ¼ 9400 K (Cox, 2000). The photometric solution was deduced from BVR observations, which are displayed in the right panel of Fig. 1. The calculation starts from Mode 2 (i.e., detached configuration), then always converges to Mode 5 (i.e., a semi-detached one). Therefore, XZ And is an Algol-type binary with the secondary filling its Roche lobe. In the absence of the spectroscopic mass ratio, the ‘‘q-search’’ process was performed to find a feasible photometric mass ratio. A series of tried solutions was made for several assumed values of q, which ranges from 0:35 to 0:70 with a step of 0:05. The resulting q R curve is displayed in the left panel of Fig. 3, where a minimum value of R is achieved at q ¼ 0:45. The mass ratio was then considered as an initial parameter for the final iteration. The photometric elements are listed in Table 3. The theoretical light curves are displayed as solid lines in the right panel of Fig. 3. The final mass ratio of qph ¼ 0:474ð0:003Þ is larger than Giuricin et al. (1980) value of 0:4. The fill-out factor is f ¼< r > =rLobe , where < r > is the average value of radii from Table 3, while r Lobe is from Eggleton (1983) 2=3
0:49q in the unit of the separation of both equation of rLobe ¼ 0:6q2=3 þln 1þq1=3
components. The fill-out factor of the primary for XZ And is f1 ¼ 68:3ð0:6Þ%. 5. Results and discussion From the previous analysis, XZ And is a classic Algol-type star, whose less massive component fills its Roche lobe. The mass ratio
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Y.-G. Yang / New Astronomy 25 (2013) 109–113
Fig. 3. Left panel: the q-R curve of XZ And. Right panel: the comparison of the observations and the theoretical light curves.
a log 3=2 h i
Table 3 Photometric elements of the algol-type binary XZ And. Parameter
ið Þ q TðKÞ X; Y xB ; yB xV ; yV xR ; yR X L=ðL1 þ L2 ÞB L=ðL1 þ L2 ÞV L=ðL1 þ L2 ÞR r(pole) r(point) r(side) r(back)
Rðo cÞ2i
Primary
Secondary
88:40ð0:13Þ 0:474ð0:003Þ 9400 þ0:662; þ0:081 þ0:717; þ0:323 þ0:627; þ0:282 þ0:505; þ0:238 3:8347ð0:0024Þ 0:9609ð0:0004Þ 0:9198ð0:0005Þ 0:8702ð0:0006Þ 0:2958ð0:0002Þ 0:3102ð0:0003Þ 0:3018ð0:0002Þ 0:3070ð0:0002Þ 0.0670
5094ð4Þ þ0:645; þ0:165 +0.849, +0.007 +0.793, +0.123 +0.708, +0.181 2.8255 0.0391 0.0802 0.1298 0:2956ð0:0002Þ 0:4239ð0:0015Þ 0:3084ð0:0002Þ 0:3410ð0:0002Þ
is qph ¼ 0:474ð0:003Þ. The O—C curve shows the secular period increasing with a light-time orbit. This situation may occur in many other Algol-type binaries, such as TT And (Erdem et al., 2007), CL Aur (Lee et al., 2010), TZ Eri (Zasche et al., 2008), and V338 Her (Yang et al., 2010), and VW Hya (Zhang et al., 2009). According to its spectral type, the mass of the primary component is M 1 ¼ 2:15 M (Popper, 1980). With Kelper’s third law of M 1 ð1 þ qÞ ¼ 0:134a3 =P2 , the separation between both components is a ¼ 8:20 R . Using the photometric elements, other absolute parameters are as follow: M 2 ¼ 1:02 M ; R1 ¼ 2:30 R and R2 ¼ 2:59 R , respectively. The cyclic oscillation for XZ And may be attributed to the lighttime effect via the presence of the third body (Irwin, 1952). The mass function of the additional component was computed by using the known formula,
f ðM 3 Þ ¼
4p2 GP 2mod
½a12 sin i ¼
ðM 3 sin iÞ
ðM 1 þ M2 þ M3 Þ2
we may conclude that XZ And should be dynamically stable. Therefore, there may exist an invisible companion in XZ And. Another possible mechanism is magnetic activity cycle, which may come from the variation of quadrupole moment DQ (Applegate, 1992). The spectral type of XZ And is A1. Thus, the magnetic activity must occur in its late-type secondary component. Using the relation of DQ DP 2pA ¼ 9 Ma (Lanza and Rodonò, 2002), we can calculate the 2 ’ P P mod value of DQ 2 ¼ 1:23ð0:03Þ 1051 g cm2 . Therefore, either cyclic magnetic activity or light-time effect may be acceptable to interpret the observed cyclic variation. From Eq. (2), the orbital period secularly increases at a rate of dP=dt ¼ þ5:37ð0:41Þ 107 d yr1 . Considering that the secondary fills its Roche lobe, mass continuously transferred from the secondary component to the primary one, which may result in the long-term period increase. Assuming the conservative mass transfer, the mass transfer rate can be calculated from the formula,
_2 P_ 3ðq 1Þ M ¼ : P q M1
ð6Þ
_ P; M 1 and q into Eq. (6), we can calculate Inserting the values of P; the mass loss rate of þ2:56ð0:20Þ 107 M yr1 . The binary XZ And, consisting of stars 2:15 þ 1:02 M with an orbital period of 1:357 days, may evolve by Low Mass Case B (Kippenhahn et al., 1967), which recently was reviewed by Shore et al. (1994). With period increasing, the separation between both components will be wider. Finally, XZ And may evolve into a binary system consisting of an A-type main sequence star plus a helium white dwarf. In the future, it is necessary to obtain high-precision photometry and spectroscopy to determine the absolute physical parameters, and to check period change and its evolutionary state. Acknowledgments
3
3
ð5Þ
M 1 þM2
;
ð4Þ
where a12 sin i ¼ A c is the projected semi-major axis of the third body. Therefore, the minimum mass of the tertiary components (i.e., i ¼ 90 ) is M3;min ¼ 1:88 M at a radius of a12 ¼ 10:7 AU. Inserting the related parameters into Harrington (1977) equation,
Many thanks are given to the anonymous referee for his/her valuable comments to improve this manuscript. This research is supported partly by the National Natural Science Foundation of China (Nos. U1231102 and 11133007), and Anhui Provincial Natural Science Foundation (No. 1208085MA04). The author would like to acknowledge Professor Kreiner for sending his compiled eclips-
Y.-G. Yang / New Astronomy 25 (2013) 109–113
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New Astronomy journal homepage: www.elsevier.com/locate/newast
A new photometry and period analysis of the Algol-type binary XZ And Y.-G. Yang ⇑ School of Physics and Electronic Information, Huaibei Normal University, 235000 Huaibei City, Anhui Province, China
h i g h l i g h t s We model new BVR light curves. We detected a periodicity in the O—C curve and provided two possible mechanisms. The secular period increase may result from mass transfer. We proposed the possible evolutionary statue.
a r t i c l e
i n f o
Article history: Received 25 March 2013 Received in revised form 30 April 2013 Accepted 6 May 2013 Available online 17 May 2013 Communicated by E.P.J. van den Heuvel Keywords: Stars: binary: close Binaries: eclipsing Stars: individual (XZ And)
a b s t r a c t We present multi-color photometry of the eclipsing binary XZ And, obtained on 2010 October and November with the 60-cm telescope at Xinglong station of National Astronomical Observatories of China. Using the updated W–D program, the photometric elements were deduced from BVR light curves. The results imply that XZ And is a classic Algol-type binary, whose secondary component fills its Roche lobe. The mass ratio and fill-out factor of the primary are q ¼ 0:474ð0:003Þ and f1 ¼ 68:3ð0:6Þ%, respectively. Based on photometric and CCD light minimum times, we constructed the O—C curve, which may be described by an upward parabolic line with a quasi-cyclic variation, i.e., light-time orbit. The period and semi-amplitude are Pmod ¼ 32:30ð0:06Þ yr and A ¼ 0:d 0368ð0:d 0008Þ, respectively. This kind of cyclic variation may result from either magnetic activity of the secondary star or light-time effect due to the unseen third body. The long-term period increases at a rate of dP=dt ¼ þ5:37ð0:41Þ 107 d yr1 , which may be interpreted by the conservative mass transfer from the secondary component to the primary one. With period increasing, the binary may become wider. Finally, XZ And (i.e., 2:15M þ 1:02M ) will transformed into a binary system consisting of a WD and an unevolved companion. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The light variability of XZ And (=BD + 41°367, aJ2000:0 ¼ 01h 56m 51:s 53 and dJ2000:0 ¼ þ42 060 02.00 15) was discovered by Miss Leavitt (Shapley, 1923). Hill et al. (1975) preliminarily determined a spectral type of A4IV-V, while Halbedel (1984) reclassified it as A1V. The variable’s magnitude ranges from 10:m 8 to 11:m 9 and the color index is B V ¼ 0:8 (Malkov et al., 2006). Visual observations were published by Leiner (1926); Kordylewska (1931); Lause (1934) and Lause (1936), respectively. Blitzstein (1954) and Reinhardt (1967) obtained two sets of photoelectric light curves, which were analyzed by Giuricin et al. (1980) who derived a mass ratio of 0.4. Dugan and Wright (1939) determined a period of 1:d 357283 and found some irregular variations in the ðO—CÞ curve. Demircan et al. (1995) summarized 16 linear ephemerides
⇑ Tel.: +86 561 3803256; fax: +86 561 3804931. E-mail address: [email protected] 1384-1076/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.newast.2013.05.001
for XZ And, implying that changes may exist in its orbital period. Based on different databases of eclipse times, several authors subsequently attempted to model the distorted ðO—CÞ curve in two ways (i.e., sine curves, and an upward parabola with a cyclic sine-shape modulation). The cyclic modulation possibly includes one period (Frieboes-Conde and Herczeg, 1973), two periods (Odinskaya and Ustinov, 1952; Todoran, 1967; Borkovits and Hegedüs, 1996; Selam and Demircan, 1999), and three ones (Demircan et al., 1995). The ðO—CÞ curve of XZ And was alternatively characterized by a secular period variation superimposed with a cyclic oscillation (Kreiner, 1971; Kreiner, 1976; Rafert, 1982). Due to those inconsistent results for XZ And, it is necessary to reanalyze the orbital period changes. In this paper, new photometry of XZ And is presented. The primary aim is to study period variation and evolutionary state. Multi-color observations and data reduction are described in Section 2. The period changes are reanalyzed in Section 3 and photometric models considered in Section 4. Finally, some results of XZ And are briefly discussed in Section 5.
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Y.-G. Yang / New Astronomy 25 (2013) 109–113
2. New observations Complete light curves of XZ And were obtained on eight nights of 2010 October and November, using the 60-cm telescope at the Xinglong station (XLs) of National Astronomical Observatories of China (NAOC). This telescope was equipped with a PI 1024 1024 CCD photometric system. The plate-scale is 0.00 99 per pixel, and the resulting size of the effective field of view is 170 170 . The standard Johnson–Cousin–Bessel set of BVRI filters was used. Data reduction was performed by using the Image Reductions and Analysis Facility (IRAF) software in the standard fashion. In the observing process, we chose BDþ41 379 and TYC 28241778-1 as the comparison and check stars. Typical exposure times for BVR bands are 45 s;35 s, 25 s, respectively. A total of 2975 effective images (i.e., 994 in B band, 989 in V band and 992 in R band) was obtained. The individual observations (i.e., HJD and Dm) are available on request. The mean errors in the differences between the magnitude of the check star and that of the comparison one were estimated to be 0:006 mag, 0:005 mag and 0:005 mag for BVR bands, respectively. The observed light curves are plotted in the left panel of Fig. 1, where phases were computed by a period of 1:d 35727963 (Kreiner et al., 2001). From this figure, XZ And is a typical EA-type eclipsing binary (Binnendijk, 1975). The variable light amplitudes are 2:m 90, 2:m 45 and 2:m 07 in BVR bands, which approximately agree with the estimated value of 2:m 97 in B band from Malkov et al. (2006). Using the 85-cm telescope (Zhou et al., 2009), another photometry of primary eclipse of XZ And was obtained on 2012 October 25, which is shown in the right panel of Fig. 1. From those observations, we determined several light minimum times, which are listed in Table 1.
Table 1 New light minimum timings of XZ And. JD (Hel.)
Min
Error
Band
2455474.35865 2455474.35847 2455474.35870 2455479.10554 2455479.10802 2455479.10332 2455481.14476 2455481.14474 2455481.14493 2455521.19063 2455521.18311 2455521.18505 2456226.29034 2456226.29029 2456226.29032
I I I II II II I I I II II II I I I
±0.00012 ±0.00014 ±0.00013 ±0.00065 ±0.00048 ±0.00074 ±0.00007 ±0.00010 ±0.00012 ±0.00149 ±0.00099 ±0.00010 ±0.00007 ±0.00008 ±0.00010
B V R B V R B V R B V R B V R
Min:I ¼ HJD2424152:2546 þ 1:d 35727963 E;
ð1Þ
we can calculate the residuals ðO—CÞ, which are listed in Table 2 and displayed in the upper panel of Fig. 2. From this figure, the general trend of the ðO—CÞ curve may be described by an upwards parabolic superimposed with a quasi-cyclic variation, i.e., a light-time orbit (Irwin, 1952). Using the nonlinear least-squares method (Press et al., 1992), we obtained the following equation,
O—C ¼ 0:0540ð0:0020Þ þ 1:35726055ð0:00000025Þ E þ 9:87ð0:08Þ 1010 E2 þ s
ð2Þ
and
1 e2 sinðm þ xÞ þ e sin x ; 1 þ e cos m
3. Reanalyzing period variations
s¼A
The complicated period variations of XZ And were studied by many authors, who gave some inconsistent results. Due to large measurement errors for visual and photographic observations, the ðO—CÞ curve could not be described well, which can be seen directly from the literature such as Borkovits and Hegedüs (1996) and Selam and Demircan (1999). Therefore, we collected all available high-precision observations, including 18 photoelectric and 48 CCD measurements. Table 2 listed those eclipsing times spanning over 64 years from 1948 to 2012. Using the linear ephemeris (Kreiner et al., 2001),
where A ¼ a12 =c is the semi-amplitude of the light-time orbit, and several other parameters are taken from Irwin (1952). The fitted parameters are listed as follows, A ¼ 0:d 0368ð0:d 0008Þ, Pmod ¼ 32:30ð0:06Þ yr; e ¼ 0:191ð0:009Þ, x ¼ 3:923ð0:047Þ and T p ¼ HJD2446108:9ð118:0Þ. The final residuals are listed in Table 2, and are shown in the lower panel of Fig. 2, where no regularity is apparent. In its upper panel, the solid and dotted lines are Eq. (2) and its parabolic part, respectively. The quadratic term represents a continuous increase of the orbital period at a rate of dP=dt ¼ þ5:37ð0:41Þ 107 d yrs1 . The modulation period is
ð3Þ
Fig. 1. Left panel: BVR light curves of XZ And, observed in 2010 using the 60-cm telescope. Right panel: the primary eclipse, obtained on 2012 October 25 using the 85-cm telescope.
111
Y.-G. Yang / New Astronomy 25 (2013) 109–113 Table 2 All compiled photoelectric and CCD eclipsing times for XZ And. JD (Hel.)
Epoch
Method
Min.
O—C
Residuals
Ref
2432883.605 2432887.676 2432955.540 2433180.847 2433206.635 2433231.7415 2439020.5507 2439033.4452 2440484.3930 2442742.2476 2443779.8763 2443809.7364 2443847.7403 2444257.6387 2444542.6659 2449313.5336 2449651.4992 2449655.5713 2450008.4732 2450430.6000 2450443.5030 2451486.6001 2451512.3884 2451881.5782 2452279.2714 2452321.3483 2452530.3718 2452534.4460 2452542.5899 2452934.8526 2452940.2820 2452949.7827 2452975.5716 2453267.3919 2453318.9701 2453335.2573 2453348.8308 2453644.7240 2453681.3712 2453715.3055 2453952.8326 2454012.5539 2454381.7406 2454429.2461 2454468.6076 2454469.2861 2454476.7520 2454708.8488 2454779.4277 2454799.7876 2454824.2181 2454863.5797 2455084.8180 2455140.4666 2455187.2939 2455239.5488 2455423.4600 2455474.3586 2455479.1056 2455481.1448 2455521.1863 2455561.2242 2455563.9386 2455842.1809 2456226.2913 2456265.6514
+6433.0 +6436.0 +6486.0 +6652.0 +6671.0 +6689.5 +10954.5 +10964.0 +12033.0 +13696.5 +14461.0 +14483.0 +14511.0 +14813.0 +15023.0 +18538.0 +18787.0 +18790.0 +19050.0 +19361.0 +19370.5 +20139.0 +20158.0 +20430.0 +20723.0 +20754.0 +20908.0 +20911.0 +20917.0 +21206.0 +21210.0 +21217.0 +21236.0 +21451.0 +21489.0 +21501.0 +21511.0 +21729.0 +21756.0 +21781.0 +21956.0 +22000.0 +22272.0 +22307.0 +22336.0 +22336.5 +22342.0 +22513.0 +22565.0 +22580.0 +22598.0 +22627.0 +22790.0 +22831.0 +22865.5 +22904.0 +23039.5 +23077.0 +23080.5 +23082.0 +23111.5 +23141.0 +23143.0 +23348.0 +23631.0 +23660.0
pe pe pe pe pe pe pe pe pe pe pe pe pe pe pe CCD pe pe pe CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD
I I I I I II II I I II I I I I I I I I I I II I I I I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I II I II I II I II I I I I I
0.0295 0.0303 0.0303 0.0317 0.0320 0.0352 0.0236 0.0233 0.0074 +0.0125 +0.0010 +0.0009 +0.0010 +0.0009 0.0006 +0.0292 +0.0322 +0.0325 +0.0416 +0.0545 +0.0633 +0.0910 +0.0910 +0.1008 +0.1110 +0.1123 +0.1147 +0.1171 +0.1173 +0.1262 +0.1264 +0.1262 +0.1268 +0.1320 +0.1335 +0.1334 +0.1341 +0.1403 +0.1410 +0.1433 +0.1464 +0.1474 +0.1541 +0.1548 +0.1552 +0.1550 +0.1559 +0.1579 +0.1582 +0.1590 +0.1584 +0.1589 +0.1606 +0.1608 +0.1619 +0.1616 +0.1614 +0.1620 +0.1585 +0.1618 +0.1635 +0.1617 +0.1615 +0.1615 +0.1618 +0.1608
0.0046 0.0053 0.0035 +0.0012 +0.0015 0.0010 +0.0054 +0.0055 0.0019 +0.0027 0.0036 0.0034 0.0029 +0.0014 +0.0035 +0.0072 +0.0001 +0.0003 0.0015 0.0017 +0.0067 +0.0027 +0.0019 +0.0012 +0.0006 +0.0008 0.0021 +0.0002 +0.0002 0.0003 0.0002 0.0006 0.0006 0.0017 0.0013 0.0017 0.0013 0.0008 0.0008 +0.0009 +0.0000 +0.0000 +0.0014 +0.0015 +0.0014 +0.0012 +0.0020 +0.0014 +0.0010 +0.0016 +0.0008 +0.0009 +0.0007 +0.0005 +0.0013 +0.0007 0.0006 0.0002 0.0037 0.0004 +0.0011 0.0009 0.0011 0.0019 0.0019 0.0029
(1) (1) (1) (1) (1) (2) (2) (3) (4) (5) (6) (6) (6) (6) (6) (7) (8) (8) (9) (10) (11) (12) (13) (14) (15) (16) (16) (17) (14) (18) (19) (20) (14) (21) (18) (22) (18) (23) (22) (22) (23) (24) (25) (26) (25) (27) (25) (28) (29) (30) (29) (30) (31) (32) (32) (31) (33) (34) (34) (34) (34) (35) (36) (36) (34) (37)
Refs. (1) Blitzstein (1954); (2) Kreiner (1976); (3) Frieboes-Conde and Herczeg (1973); (4) Pohl and Kizilirmak (1970); (5) Brancewicz and Kreiner (1976); (6) Olson (1981); (7) Hawkins and Downey (1994); (8) Hegedüs et al. (1996); (9) Müyesseroglu et al. (1996); (10) Baldwin and Samolyk 1997; (11) Paschke (1999); (12) Baldwin and Samolyk (2000); (13) Agerer and Hübscher (2001); (14) Baldwin and Samolyk (2004); (15) Diethelm (2002); (16) Agerer and Hübscher (2003); (17) Borkovits et al. (2003); (18) Cook et al. (2005); (19) Hübscher (2005); (20) Nelson (2004); (21) Hübscher et al. (2005); (22) Hübscher et al. (2006); (23) Baldwin and Samolyk (2007); (24) Biró et al. (2007); (25) Samolyk (2008a); (26) Hübscher et al. (2008); (27) Brát et al. (2008); (28) Samolyk (2008b); (29) Hübscher et al. (2009); (30)Samolyk (2009); (31) Samolyk (2010); (32) Erkan et al. (2010); (33) Dogru et al. (2011); (34) Present work; (35) Brát et al. (2011); (36) Nagai (2012); (37) Diethelm (2013).
Fig. 2. The O—C curve of the eclipsing binary XZ And. The filled circles represent photoelectric or CCD observations. The solid and dotted lines are constructed by all the contribution of Eq. (2) and only its parabolic part, respectively.
a bit smaller than the value of 35:6 yr from Borkovits and Hegedüs (1996). 4. Photometric solution Multi-bandpass observations of XZ And were simultaneously analyzed using the 2003-version W–D program (Wilson and Devinney, 1971; Wilson, 1990), which is widely used for modeling the photometric light curves of eclipsing binaries as a standard tool. The bolometric albedos and gravity darkening coefficients were adopted as A1 ¼ 1 and g 1 ¼ 1 for the primary with radiative envelope, A2 ¼ 0:5 and g 2 ¼ 0:32 for the secondary with radiative one (Lucy, 1967; Rucinski, 1969; and von Zeipel, 1924). Meanwhile, the logarithmic bolometric (X and Y) and monochromatic (x and y) limb-darkening coefficients were taken from the tables of van Hamme (1993). During the calculation, the five adjustable parameters i, q; T 2 ; X1 , and L1 were used. According to the spectral type A1 of XZ And (Halbedel, 1984), the mean effective temperature of the primary component was fixed to be T 1 ¼ 9400 K (Cox, 2000). The photometric solution was deduced from BVR observations, which are displayed in the right panel of Fig. 1. The calculation starts from Mode 2 (i.e., detached configuration), then always converges to Mode 5 (i.e., a semi-detached one). Therefore, XZ And is an Algol-type binary with the secondary filling its Roche lobe. In the absence of the spectroscopic mass ratio, the ‘‘q-search’’ process was performed to find a feasible photometric mass ratio. A series of tried solutions was made for several assumed values of q, which ranges from 0:35 to 0:70 with a step of 0:05. The resulting q R curve is displayed in the left panel of Fig. 3, where a minimum value of R is achieved at q ¼ 0:45. The mass ratio was then considered as an initial parameter for the final iteration. The photometric elements are listed in Table 3. The theoretical light curves are displayed as solid lines in the right panel of Fig. 3. The final mass ratio of qph ¼ 0:474ð0:003Þ is larger than Giuricin et al. (1980) value of 0:4. The fill-out factor is f ¼< r > =rLobe , where < r > is the average value of radii from Table 3, while r Lobe is from Eggleton (1983) 2=3
0:49q in the unit of the separation of both equation of rLobe ¼ 0:6q2=3 þln 1þq1=3
components. The fill-out factor of the primary for XZ And is f1 ¼ 68:3ð0:6Þ%. 5. Results and discussion From the previous analysis, XZ And is a classic Algol-type star, whose less massive component fills its Roche lobe. The mass ratio
112
Y.-G. Yang / New Astronomy 25 (2013) 109–113
Fig. 3. Left panel: the q-R curve of XZ And. Right panel: the comparison of the observations and the theoretical light curves.
a log 3=2 h i
Table 3 Photometric elements of the algol-type binary XZ And. Parameter
ið Þ q TðKÞ X; Y xB ; yB xV ; yV xR ; yR X L=ðL1 þ L2 ÞB L=ðL1 þ L2 ÞV L=ðL1 þ L2 ÞR r(pole) r(point) r(side) r(back)
Rðo cÞ2i
Primary
Secondary
88:40ð0:13Þ 0:474ð0:003Þ 9400 þ0:662; þ0:081 þ0:717; þ0:323 þ0:627; þ0:282 þ0:505; þ0:238 3:8347ð0:0024Þ 0:9609ð0:0004Þ 0:9198ð0:0005Þ 0:8702ð0:0006Þ 0:2958ð0:0002Þ 0:3102ð0:0003Þ 0:3018ð0:0002Þ 0:3070ð0:0002Þ 0.0670
5094ð4Þ þ0:645; þ0:165 +0.849, +0.007 +0.793, +0.123 +0.708, +0.181 2.8255 0.0391 0.0802 0.1298 0:2956ð0:0002Þ 0:4239ð0:0015Þ 0:3084ð0:0002Þ 0:3410ð0:0002Þ
is qph ¼ 0:474ð0:003Þ. The O—C curve shows the secular period increasing with a light-time orbit. This situation may occur in many other Algol-type binaries, such as TT And (Erdem et al., 2007), CL Aur (Lee et al., 2010), TZ Eri (Zasche et al., 2008), and V338 Her (Yang et al., 2010), and VW Hya (Zhang et al., 2009). According to its spectral type, the mass of the primary component is M 1 ¼ 2:15 M (Popper, 1980). With Kelper’s third law of M 1 ð1 þ qÞ ¼ 0:134a3 =P2 , the separation between both components is a ¼ 8:20 R . Using the photometric elements, other absolute parameters are as follow: M 2 ¼ 1:02 M ; R1 ¼ 2:30 R and R2 ¼ 2:59 R , respectively. The cyclic oscillation for XZ And may be attributed to the lighttime effect via the presence of the third body (Irwin, 1952). The mass function of the additional component was computed by using the known formula,
f ðM 3 Þ ¼
4p2 GP 2mod
½a12 sin i ¼
ðM 3 sin iÞ
ðM 1 þ M2 þ M3 Þ2
we may conclude that XZ And should be dynamically stable. Therefore, there may exist an invisible companion in XZ And. Another possible mechanism is magnetic activity cycle, which may come from the variation of quadrupole moment DQ (Applegate, 1992). The spectral type of XZ And is A1. Thus, the magnetic activity must occur in its late-type secondary component. Using the relation of DQ DP 2pA ¼ 9 Ma (Lanza and Rodonò, 2002), we can calculate the 2 ’ P P mod value of DQ 2 ¼ 1:23ð0:03Þ 1051 g cm2 . Therefore, either cyclic magnetic activity or light-time effect may be acceptable to interpret the observed cyclic variation. From Eq. (2), the orbital period secularly increases at a rate of dP=dt ¼ þ5:37ð0:41Þ 107 d yr1 . Considering that the secondary fills its Roche lobe, mass continuously transferred from the secondary component to the primary one, which may result in the long-term period increase. Assuming the conservative mass transfer, the mass transfer rate can be calculated from the formula,
_2 P_ 3ðq 1Þ M ¼ : P q M1
ð6Þ
_ P; M 1 and q into Eq. (6), we can calculate Inserting the values of P; the mass loss rate of þ2:56ð0:20Þ 107 M yr1 . The binary XZ And, consisting of stars 2:15 þ 1:02 M with an orbital period of 1:357 days, may evolve by Low Mass Case B (Kippenhahn et al., 1967), which recently was reviewed by Shore et al. (1994). With period increasing, the separation between both components will be wider. Finally, XZ And may evolve into a binary system consisting of an A-type main sequence star plus a helium white dwarf. In the future, it is necessary to obtain high-precision photometry and spectroscopy to determine the absolute physical parameters, and to check period change and its evolutionary state. Acknowledgments
3
3
ð5Þ
M 1 þM2
;
ð4Þ
where a12 sin i ¼ A c is the projected semi-major axis of the third body. Therefore, the minimum mass of the tertiary components (i.e., i ¼ 90 ) is M3;min ¼ 1:88 M at a radius of a12 ¼ 10:7 AU. Inserting the related parameters into Harrington (1977) equation,
Many thanks are given to the anonymous referee for his/her valuable comments to improve this manuscript. This research is supported partly by the National Natural Science Foundation of China (Nos. U1231102 and 11133007), and Anhui Provincial Natural Science Foundation (No. 1208085MA04). The author would like to acknowledge Professor Kreiner for sending his compiled eclips-
Y.-G. Yang / New Astronomy 25 (2013) 109–113
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